Evaluate: `intsin^4x\ dx`

Explanation

`intsin^(4)xdx=(1)/(4)int(2sin^(2)x)^(2)dx`
`=(1)/(4)int(1-cos2x)^(2)dx=(1)/(4)int(1+cos^(2)2x-2cos2x)dx`
`=(1)/(8)int(2+2cos^(2)2x-4cos2x)dx`
`(1)/(8)int[(2+(1+cos4x)-4cos2x]dx`
`=(3)/(8)intdx+(1)/(8)intcos4xdx-(1)/(2)intcos2xdx`
`=(3)/(8)x+(sin4x)/(32)-(sin2x)/(4)+C`.